If you want to add an extra layer of dirt to your guitar sound then you need to explore the world of drive pedals, and there are few different flavours to consider. Most commonly you'll be looking at boost, overdrive, distortion and fuzz. Each one adds a different layer of filth to your guitar sound.
Boost does exactly what it sounds like. It boosts the signal from your guitar, thus driving the front of your amp harder, allowing your riffs and solos to really push through the mix.
Overdrive is designed to hit the front of your amp harder still, whilst still maintaining the character of your guitar's tone. Overdrive is typically used in classic rock and blues styles.
Distortion has a harder, more aggressive sound, found more commonly in metal, hard rock and punk.
Fuzz is neither subtle, nor is it polite, but it does offer gain in spades and has been used to devastating effect since the birth of rock.