The self loading rifle is a rifle with a semi automatic action - that is, once the weapon is cocked and the safety released, each pull of the trigger will fire the chambered round and then cycle the action, ejecting the spent case and chambering a new round from the magazine. This will continue with every trigger pull unless the weapon malfunctions or is made safe, or until there is no more ammunition in the magazine. Confusingly, some early sources refer to this as 'automatic' action (or some variation thereon) - much the same problem as is faced around the self loader pistol.
This was normally a stepping stone between the bolt action rifle and the assault rifle for most nations - during WW2 the USSR, USA and Germany all fielded 'full power' self loading rifles (the M1 Garand, the Ge41/43 and the SVT40 respectively - amongst others) and even after the war the retention of "full power" ammuntion resulted in several nations failing to field an assault rifle and instead deploying a new semi-automatic weapon (interestingly the US M-14 and the British L1, which both fall into this category, were both modified assault rifles - or, arguably battle rifles - with the fully automatic action deleted). In some cases these weapons (or direct variants of them) were retained once the nations in question finally fielded a "reduced power" assault rifle (e.g. the US retaining the M14 variant M21) as a 'designated marksman' weapon to provide longer range fire support.
Non-"Full power" semi-automatic rifles were also developed in the post WW2 period, either for civilian/police use (like the Ruger Mini-14 - an M14 re-engineered in 5.56NATO) or for military use (like the Simonov SKS in 7.62mmWarPac) and these, as well as some full power designs are still in civilian use except in those countries with oppressive firearms law.
Anti material rifles are also still being built in this format.