1. slowly (but steadily); gradually; bit-by-bit
じりじりと敗北が近づいてくる。Defeat is slowly but steadily approaching.
Adverb
Verb (する)
Onomatopoeic
2. irritatedly; impatiently
じりじりしながら、ときが過ぎるのを待つ。I wait impatiently for the time to pass.
3. scorchingly (of the sun)
吹き出す汗も、肌をじりじりと焼く強い日差しも気にならない。I don't mind the sweat breaking out or the strong sunlight scorching my skin.
4. sizzling (i.e. sound of frying in oil)
5. sound of a warning bell, alarm clock, etc.
じりじりと列車のベルが鳴る。The train's bell rings with a jangling sound.
6. oozing out (oil, sweat, etc.); seeping out