Burstable RAM is a term used in the VPS industry to describe extra RAM set aside for high-traffic needs. Providers will often advertise a given amount of RAM on a VPS (256 MB, for example), but say it is burstable up to 384 MB. This means you will always have 256 MB of RAM, but may be able to use a much as 384 MB.
The amount of burstable memory that can be used depends on the loads of the other VPS units sharing your parent server. If the other clients are using all available resources, little burstable RAM will be available. On the other hand, you may find you can use all or most of it if the other units are running far below capacity.