Meaning of causal signal
A causal system (e.g. a causal filter) is as you say, it simply depends on only past and present values of the input.
All real time systems are causal, for they cannot "see" the future", i.e. it is not possible to have an output before there has been an input.

An example of a non-causal system would be:

y(t) = x(t + 5)

An example where non-causality comes into use is something like an ideal filtering system applied at a later time, where the data has been recorded previously (or is estimated in the case of predictive systems), therefore the future state of the input is known.