What does it mean the security parameter for a FHE scheme? FHE schemes claim to use some security parameter $\lambda$ for deriving the other parameters of the scheme, the size of the key and the possible circuits that can be evaluated. Like in Fully Homomorphic Encryption over the Integers. What does this parameter signify ?

Is something that applies only to FHE schemes and puts them on hierarchy of security ? How does this parameter compare to classical schemes, like RSA or AES ?
How can be compared the security of a FHE scheme with RSA or AES ?
What does this parameter signify ?


It's a tweakable parameter that varies (typically) the sizes of various objects in the cipher, and while any non-silly value will work (e.g. encrypt and decrypt properly), it does have an influence on the security of the system (typically, how hard of a 'hard problem' the system relies on).


  Is something that applies only to FHE schemes and puts them on hierarchy of security ?


Actually, it's fairly common for public key systems to have such a parameter; it's not limited to FHE systems.


  How does this parameter compare to classical schemes, like RSA or AES ? 


Actually, RSA does have a 'security parameter'; it's the modulus size.  When you generate an RSA keypair, you select the size of the modulus; that's your security parameter.  Now, we typically don't call that a security parameter, however I believe that's for mostly historic reasons; RSA predates much of modern nomenclature, and so uses its own terminology.

As for AES, no, it doesn't - AES comes in three flavors (128 bit keys, 192 bit keys, 256 bit keys), and those are the only variations you are allowed.

Symmetric ciphers, in generally, usually don't have security parameters; I suspect that's because they're not usually based on preexisting 'hard problems' (and so don't need to choose the size of hard problem to rely on).