Hi,
Online estimation is estimating the parameters during the operation of the physical system as new data becomes available. For example, trying to extract motor winding resistance while spinning the rotor. As you can see, we have constraints, we need to get the estimation at specific time instants and the complexity of the algorithm is limited by the embedded system specification.
On the other hand, offline estimation does not require the physical system to be in operation during the estimation process. It is usually based on data that is already available in advance. For example, we do some experiments and measure relevant signals then we analyse the data and estimate relevant parameters on personal computer afterwards. When we have a good set of parameters, we go an operate the physical system. In offline estimation the complexity of the algorithm is not that important as we can spend days until we get a good set of parameters.
I hope this helps.