Isothermal means "at fixed temperature".
This is to contrast with the more well established polymerase chain reaction, which requires heating and cooling the sample several times.
The obvious advantage of isothermal methods is that their machinery can be simpler and cheaper, and the process can happen faster, since you don't have to do through heating and cooling cycles.
Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Video 1. Loop Mediated Isothermal Amplification (LAMP) Tutorial by New England Biolabs (2015) Source. Explains the basic LAMP concept well.