When a domain name expires you can sometimes bid for it in auction.

However, many domain names never go to auction. Instead, they expire and are dropped allowing a user to register them for about $10 (the registration fee).

BUT, if someone else wants the same domain name as you they are likely to try to register it with an automated service – called a dropcatching service.

And let’s face it…computers are faster than us and can see if the domain name is available every second of the day; we have to sleep. To compete with them, you can pay about $60 and hire a backorder service (also known as a dropcatching service) to do the same on your behalf.

Notes:
Some of these services charge to place the domain name backorder, while others only charge you if a backorder is completed. Do your due diligence.
If more than one backorder is placed at any service, it’s likely to go to a closed auction at that service provider; in some cases, it goes to the first backorder.
No single service provider can guarantee acquisition and – due to many factors – no one service provider is better at acquisition than another. If you really want a domain name, put in a backorder at all of them.

Here is a list of backorder services that you may want to investigate (in alphabetical order):

• BackorderZone
  Free backorder with credit card on file; only pay upon successful registration, com/net: $49
• GoDaddy Backoder
  With GoDaddy Domain Backorders, you choose the name and we’ll put you in position to get it. Just choose your .COM, .CO, .INFO, .ORG, .NET, .ME, .MOBI, .US, or .BIZ and we’ll do the rest – it’s that easy! Find out below how the backorder process works.
• DomainMonster
  Free backorder; only pay upon successful registration, com: £39.99 (other TLD pricing listed)
• DropCatch
  Free backorder; only pay $69 upon successful registration (if more than one backorder, it goes to public auction where anyone can join)
• Dynadot
  com: $14.99, net: $14.99, org: $14.99
• Go Daddy
  Pre-pay $24.98 (or less) and use until successful for com, co, info, org, net, me, mobi, us and biz
• Hexonet
  Free backorder; only pay $69 upon successful registration but must have sufficient funds in your account (prepaid)
• NameCatch
  .in backorder and drop-catch service; $19.99 to place backorder with 100% satisfaction guarantee
• NameJet
  Free backorder; only pay $69 upon successful registration (if more than one backorder, it goes to private auction)
• Nidoma
  Free backorder; only pay 29€ upon successful registration; .es and .it domains
• Park.io
  Free backorder; only pay $99 upon successful registration; .io, .ly and .me domains
• Pheenix
  com: $21.95, net: $21.95, org: $21.95, tv: $58.95, cc: $58.95
• Pool
  Free backorder; only pay $60 upon successful registration
• SnapNames
  Free backorder; only pay $69 upon successful registration (if more than one backorder, it goes to private auction)

Source: http://www.domainsherpa.com/domain-name-backorder-services/