There are several ways to prioritize the requirements in the backlog. Some of the most popular ones include,

MoSCoW

M - MUST have this.
S - SHOULD have this if at all possible.
C - COULD have this if it does not effect anything else.
W - WON'T have this time but would like in the future.

Each requirement will have the priority which would be tagged to MSCW. “M” being the highest and “W” being the lowest.

This site gives a very good explanation about this technique.

Business Value Based

In this case, each requirement carries a business value it could potentially generate to the company. The business value would be decided either by the Product Owner or the Product owner team.

The requirement with highest business value is implemented during earlier releases .

Technology Risk Based

In this method, requirements are prioritized based on the risk associated in implementing it. The risk is typically based on the technology.

The requirement with highest technology risk is implemented during the earlier iterations.

Kano Model

In this method, the requirements are prioritized based on the customer preferences.

• Attractive
• One-Dimensional
• One-Dimensional
• Must-Be
• Indifferent
• Reverse

You can read more details about this model here

Walking Skeleton

In this method, the requirements are selected such that minimal carefully selected end to end features are built within a short span of time.

Validated Learning

In this method, features are chosen based on the highest market risk i.e. some thing that is not experimented yet. Release it to the market, get the feedback and apply the learning onto the new feature.

This deck gives a good view about validated learning in the context of lean startup