modulo operations in crypto algorithms Am not a mathematician. 

Every crypto specification I see uses the modulo operation. For example RSA - 

If $e$ is the public key and $m$ is the plaintext with a modulus $n$ - the cipher text is $c = m^{e} \bmod n$

Why is this $\bmod\ n$ there? By definition isn't the modulo operation introduces an uncertainty? I mean  $3 \bmod 7 = 10 \bmod 7 = 3$. 

Is it the idea to limit the result to a group? Why is there no uncertainty about the result?
Is it the idea to limit the result to a group?

Yes. The advantage to doing so is that we have multiplicative inverses (well, for anything relatively prime to $n$) and can therefore decrypt. It also keeps ciphertexts relatively small.

Why is there no uncertainty about the result?

There would be, except we require require plaintexts to be smaller than the modulous (i.e., part of the group). In your example, we wouldn't allow 10 to be a plaintext, because 10 is greater than 7, the modulous.

So how do you encrypt long messages? Normally, the only thing you encrypt using RSA is a symmetric key, and then encrypt your actual message using the symmetric key. Since symmetric keys are significantly shorter than RSA moduli, this isn't an issue.

We would also like to sign long messages with RSA. Therefore we typically hash the message to a digest that's shorter than the modulous, and then sign the digest. This also improves performance and stops attackers from exploiting the fact that RSA encryption is a homomorphism to forge signatures.