1. Definition of 'Real-time': the actual time during which a process or event occurs. Or, the actual time during which something takes [Merriam-Webster dictionary]
2. There are many 'real-time' techniques used in biological researches nowadays. Depend on which one you are talking about. For example, (1) we have real-time PCR (or called qPCR). (2) Another example, through advanced imaging technology, you can monitor the movement of a GFP-fused protein in 'real-time' under a specific microscope. (3) And, using confocal microscope to monitor virus spread in plant leaves in real-time (see below attachment). (4) Another case is 'CRISPR imaging'. Modified Cas9 (dCas9) from CRISPR/Cas9 system was tagged to eGFP (dCas9::eGFP) and used to direct recording of real-time dynamic events in living cells. There are many other cases.
it is PCR but the advantage is that you can monitore progress of PCR amplification during the reaction based on increasing fluorescence. The measurement is made every PCR cycle - so you can see a amplification curve. At the end you can do also melting curve analysis.
This is very useful material which can introduce you this method.