Short answer: agate is a variety of chalcedony, which is quartz with crystals too small to see. What makes a stone an agate rather than plain chalcedony is its banding: layers of slightly different colour or translucency laid down as the stone formed. It is hard (6.5 to 7 on the Mohs scale), it takes a high polish, and it has been cut for seals and rings for at least four thousand years.
What agate actually is
Agate forms in cavities in volcanic rock. Silica-rich water seeps in and deposits quartz layer by layer on the cavity walls, so a cut agate shows concentric bands like tree rings. The bands can be fine enough to look like a single colour, or bold and contrasting. Because the quartz is microcrystalline, agate is tough as well as hard: it does not cleave along planes the way many crystals do, which is one reason it has survived so well as a ring stone.
Colours, and what "dyed" means
Natural agate is mostly grey, white, pale blue and brown. Strong black, bright blue, green and pink agates are usually dyed. This is not a modern trick: agate has been dyed since Roman times, and because the stone is porous in layers the colour goes deep and is stable. It is an accepted treatment in the trade, but it should be stated. Red and orange agate without banding is usually sold as carnelian; red agate from Yemen, known in Arabic as aqeeq, has its own long tradition in rings across the Islamic world. Where a stone in one of our rings is dyed or is a created stone, the product page says so.
Which zodiac sign is agate linked to?
There is no single answer, because there is no single list. The zodiac and birthstone tables used today were drawn up by jewellers' associations in the twentieth century, and older tables from different countries give different stones for the same sign. In the most widely printed Western lists, agate is the stone of Gemini (21 May to 20 June). Some lists give it to Taurus or Virgo instead, and some place it as the stone for the month of May or June rather than for a sign. In Turkish and Middle Eastern tradition, agate is valued less by zodiac and more as a protective stone in its own right, which is why it is one of the classic stones for a man's ring.
Treat these associations as tradition, not as a property of the stone. If you like agate, your sign does not have to match.
How to care for agate
Agate is one of the easier stones to live with. It can be washed in warm water with a little mild soap and a soft brush, and it does not mind being worn every day. Keep it away from strong household chemicals and from hard knocks on the edge of the stone, where a chip is possible despite the hardness. Dyed agate is best not left in direct sun for long periods. Store it separately from harder stones such as sapphire, which can scratch it.
In short
Agate is banded quartz: hard, tough and made for rings. Bright colours are usually dyed and should be declared. The zodiac link most people mean is Gemini, but it is a tradition, not a rule.