An escalation is an increase or growth. When there's an escalation in tension between two countries, it means that things have become much more strained between them.
An escalation in Christmas tree prices means that your holiday decor will be more expensive this year, and an escalation of violence in a particular country will probably keep you from traveling there until things calm down. When something gets bigger or more intense, there's an escalation. The word comes from the verb escalate, which in turn is a back-formation from escalator. The Latin root of all three words is scala, or "ladder."