Single option or single-leg option is the very basic strategies which have only one leg. You buy a single option (long call, long put), or you sell a single option (short call, short put).
A leg in options trading is a name for the individual component options that makes up an options strategy. When you simply buy or write a single options contract, you are executing a single legged options strategy. This means an options strategy that comprises of only one component options contract regardless of how many contracts are being traded. Buying one contract of call options is a single legged options strategy (long call) and buying ten contracts of that same call options is still a single legged options strategy as only one specific call options contract is involved in that options position. Basically, "legs" are used to describe the number of component options in an options strategy.
A long call gives you the right to buy the underlying stock at strike price. It is usually placed when you expect the underlying stock to increase in value before expiration.
A long put gives you the right to sell the underlying stock at strike price. It is usually placed when you expect the underlying stock to decrease in value before expiration.
Selling the call obligates you to sell stock at strike price if the option is assigned.
Selling the put obligates you to buy stock at strike price if the option is assigned.