Angel capital fills the gap in start-up financing between the "three F" (friends, family and fools) and venture capital. Most venture capital funds will not considere investments under $1 million, while it is difficult to raise more than $100,000 - $200,000 from friends and family. Thus, angel investment is a common second round of financing for high-growth start-ups.
Angel investments bear extremely high risk, and thus require a very high return on investment. Typical angel investments require a return of at least 15-20 times the original investment within 5 years, as well as an exit strategy - plans for an IPO or an acquisition. Angel financing is thus one of the most expensive sources of funds. However, cheaper sources of capital, such as bank financing, are not available for most early-stage ventures.
Angel investors are often retired business owners or executives, who are looking for a "hobby", not just monetary return. Thus, aside from funds, angel investors can sometimes provide valuable management advice and important contacts.