Step 1: compare two kinds of ligand.
Imagine attaching ligands to a metal in two ways. In one, you use several separate single-toothed ligands, each gripping with one point. In the other, you use a single ligand that has two or more teeth and so wraps around the metal forming a ring. The ring-forming kind makes the complex noticeably more stable.
Step 2: define the chelate effect.
This extra stability that a ring-forming (chelating, polydentate) ligand gives to a complex, compared with a similar complex built from single-toothed (monodentate) ligands, is called the chelate effect. The rings act like a clasp that holds the metal firmly.
Step 3: back it with an example.
Take $\mathrm{[Ni(en)_3]^{2+}}$, in which three 'en' molecules each form a ring around nickel. It is distinctly more stable than $\mathrm{[Ni(NH_3)_6]^{2+}}$, where six separate ammonia molecules just touch the metal at one point each.
So chelating ligands grant extra stability, as in [Ni(en)₃]²⁺ being more stable than [Ni(NH₃)₆]²⁺.