The mechanism involves a chain reaction. During a chain reaction, for every reactive species you start off with, a new one is generated at the end - and this keeps the process going. The over-all process is known as free radical substitution, or as a free radical chain reaction.
1) Chain initiation: The chain is initiated (started) by UV light breaking a chlorine molecule into free radicals
Cl2→2Cl.
2) Chain propagation reactions: These are the reactions which keeps the chain going.
CH4+Cl.→CH.3+HCl
CH.3+Cl2→CH3Cl+Cl.
3) Chain termination reactions: These are reactions which remove free radicals from the system without replacing them by new ones
2Cl.→Cl2
CH.3+Cl.→CH3Cl
CH.3+CH.3→CH3CH3