Per request, I post my comment(s) as an answer, and add some further remarks.
The notation $\rm\ a\ mod\ b\ $ denotes the remainder when dividing $\rm\,a\,$ by $\rm\,b\,$ using the division algorithm. The same notation is used in other domains that have an analogous (Euclidean) Division Algorithm, e.g. polynomials with coefficients over a field.
Also "mod" is also as a ternary relation (vs. binary operation) when dealing with congruence relations, e.g. $\rm\ a\equiv b\pmod n\iff n\mid a-b.$
The operational use of mod is often more convenient in computational contexts, whereas the relational use often yields more flexibility in theoretical contexts. The difference amounts to whether it is more convenient to work with canonical normal forms, or arbitrary equivalence classes. For example, imagine how inconvenient it would be to state the laws of fraction arithmetic if one required all fractions to be in normal (reduced) form, i.e. in lowest terms. Instead, it proves very flexible to work with arbitrary equivalent fractions, e.g. to choose both with a common denominator before adding fractions.
The use of the percent sign to denote mod (as in the C programming language) has not percolated to be standard in the mathematical community as far as I can tell. I recall many questions on sci.math regarding the meaning of $\rm\, a \% b.\, $ As such, if you use this notation in a mathematical forum then I recommend that you specify its meaning. This would not be necessary for "mod", since that notation is ubiquitous in mathematics. Be aware, however, that some mathematicians look down on the operational use of mod in the case when it would be more natural to use the congruence form. Apparently the mathematical Gods do too, since doing so can make some proofs quite more difficult (much more so than the simple fractional example mentioned above).