What does this equation about DNA replication mean?
The notation you are referring to is a way to express the elongation of a nucleotide strand (Fig. 1).

dNTP + dNMP(n) → dNMP(n+1) + PPi   

means

Existing strand  +  deoxynucleotidetriphosphate  →  elongated-strand  +  pyrophospate.

  

Fig. 1. Elongation of DNA. Source: Concepts in Genetics.



This reaction holds for DNA replication as well as transcription. 

Translation is all about protein synthesis from amino acid precursors. Each subsequent amino acid is coupled to the growing peptide by a peptide bond between the carboxyl of the growing peptide and the amino group of the new amino acid. A water molecule is eliminated during the reaction (Fig. 2).


Fig. 2. Peptide bond formation. Source: An Introduction to Molecular Biology

Hence translation can be written analogously to replication as:


amino acid + peptide(n) → peptide(n+1)  

However, also in this polymerization reaction energy is needed and amino acids are activated while they are bound to the messenger RNA (mRNA) through the action of ATP. Moreover, during translation the ribosome (i.e., the protein synthesizing machinery) uses another source of energy to move across the RNA template, namely GTP. Hence, the net reaction can be written as:


amino acid + peptide(n) + ATP + GTP → peptide(n+1) + AMP + GDP + PPi + Pi 

Note that this notation in itself is not a dogma as other ways are in use to denote DNA and RNA synthesis. According to Merriam-Webster a dogma is:


  A belief or set of beliefs that is accepted by the members of a group without being questioned or doubted.