Although analog audio signals travel instantaneously through mixing consoles, signal processors and effects units, digital signals take a while to calculate.
So if you insert a plug-in into a channel in your multitrack recording software, it will delay the signal probably by at least a millisecond or so, maybe more.
It's worth considering whether this will have any detrimental effect on your sound.
Mostly, it won't make any noticeable difference. In terms of rhythmic tightness, if you consider that much MIDI music of the past has been produced at a resolution of 96 pulses per quarter note, then this represents a timing accuracy of around 5 milliseconds at a moderate tempo.
Some people did complain that this resolution wasn't fine enough, but it didn't affect record sales in the slightest.
So we can take 5 milliseconds as a benchmark. Few people will notice an inaccuracy finer than this, but push the figure much higher and it really will start to become a problem.
The fact is that systems that have DSP (digital signal processing) chips available will suffer far less from plug-in delay, to the point where rhythmic accuracy is not a problem. But there can be other problems.
For example, if one channel of a stereo signal needs processing, then to insert a plug-in into that channel will cause a delay. Even if this delay is as short as 25 microseconds, this will affect the audio and cause cancellation of some frequencies.
The solution is to insert the same plug-in into both channels, but use neutral settings on the channel that doesn't need to be processed.
In 'host-based' systems, where the computer's processor does the grunt work, then delay is more of a problem, and the 5 millisecond benchmark will be breached frequently. For slowly-changing pad sounds, 5 milliseconds is neither here nor there. But for precise rhythmic tracks, anything even a little over will make an audible difference.
Ultimately, the answer will be systems that feature automatic delay compensation. This delays every track by the maximum delay caused by the plug-ins on any one track. In some systems, this happens during track bouncing, so that the bounced version might sound different to the multitrack version you have become accustomed to.
Of course, delay compensation can be done manually – simply slide an offending track to an earlier point on the timeline.
One day, delay compensation will be a thing of the past and we never have to worry about it. But for the present, unless you have DSP, it is something you need to consider pretty much all the time.