What is the definition of a mutation?
Good question!

The term mutation can be used with two different meanings. Each definition can further be split into two different more detailed definitions. The reason for this slight mess is mainly historical. In short, a mutation can refer to


An event


narrow sense
broad sense

An allele


definition based on ancestral/derived states
definition based on frequency



Before going into the details of these definitions, it is important to first define a few other terms.

A few other definitions

The terms I want to define here are Locus, polymorphic locus, allele, nucleotide and phenotype.

In short (simplified version), a phenotype is the way an individual look. The variations of phenotypes of the individuals in a population depends upon the variation of genotypes and the variation of environments that they encounter. This concept is very much related to the concept of heritability. You may want to read more about it here.

The DNA sequence is made of four nucleotides. It is the sequence of these nucleotides that affect the phenotype of an individual

A locus is refers to the position of a DNA sequence of arbitrary length. At a given locus different types of sequence can exist, such a coding or non-coding sequence, a gene or just an intron, only a few codons, etc..

An allele is one variant of a sequence (often a gene) at a given locus. If, in the population, more than one allele exists at a given locus, than the locus is said to be polymorphic. Most polymorphic loci have only two alleles. In such case we can talk about bi-allelic loci.

Mutation as an event

A mutation can refer to an event.

Narrow definition

A mutation may refer to the event of a spontaneous change in the nucleotide sequence of an individual such as typically an indel (insertion or deletion of one or few nucleotides) or a substitution (substitution of a nucleotide by another one). In other words, a mutation can refer to the event of changing allele (eventually making up a new one) at a given locus.

Broad definition

The broad definition is similar to the narrow one expect that it encompass more types of genetic changes. In the broad sense, a mutation may refer more globally to any genetic spontaneous change. For example a whole chromosome deletion or a full genome duplication are examples of mutations.

In my experience, most often when the term "mutation" is used, it is to refer to the broad definition of mutation.

Mutation as an allele

A mutation can refer to an allele. Note however that very often we prefer using the terms "mutant allele", "mutant state" or just "mutant" as synonym to refer to this allele. Pretty much the only circumstance in which we would use the term mutation here is in sentences of the kind "Individual A carries the mutation.".

Definition based one ancestral/derived states

A mutation can refer to the allele that is derived from a more ancestral allele. Consider for example, a given locus was NOT polymorphic in the past. A mutation (in the sense of "event") occurs and the locus is now polymorphic. The allele that has been created by the mutation (in the sense of "event") is sometimes called "mutation".

Definition based on frequency

A mutation can refer to the allele that is at the lowest frequency in the population. For example, consider a bi-allelic locus with two alleles A and B. If the frequency of the allele B is lower than $\frac{1}{2}$ (that is lower than the frequency of the allele A), then the allele B can be referred to as the mutation. The reason for calling "mutation" the allele that is at low frequency is that most mutations are deleterious and as a consequence the mutant allele is often at low frequency. As a consequence, using the Definition based on frequency and Definition based one ancestral/derived states is often not important.

To address your question specifically

It is a little hard to directly address your question as it seems to have several misunderstanding on the concept of mutation. In the same time however, it feels like you are turning around the realization that there are several definitions in use.


  Sometimes you encounter the terminology that one has a mutation on both alleles (father's and mother's side). But why is that called a mutation and not just a variation? 


The term mutation (whichever definition you pick) is intrinsically related to the concept of variation in the population but not so much to variation within a single individual (homozygote vs heterozygote).

If an individual "has a mutation on both allele", refers to the term mutation as an allele (in the narrow sense probably) and not as an event. More specifically it refers to one allele at a polymorphic locus (probably a locus of only one nucleotide) within the allele considered at the larger polymorphic locus considered.


  Does a mutation mean that it changed during lifetime


A mutation (in the sense of event) is a change that if often view at the moment of reproduction but the mutation may have occurred anytime in the lineage of the germ cells. Note, one may consider also mutation that occurred (during the lifetime of the individual) but in the soma cells. Such mutation will NOT be transmitted to the offspring.


  Or is there really a kind of standard taken where deviations are considered to be mutations?


Well...yes! A deviation is a deviation to a reference. In other words, we can replace "deviation" by "one allele of a polymorphic locus" in your question. And yes, a mutation (in the sense of a given allele) can refers to one allele of a polymorphic locus.