Mobility allowance is for covering the costs of relocation or commuting when you accept a new job. As a member of a unemployment fund you apply for allowance from the fund. If you aren't yet a member of a unemployment fund apply for allowance from Kela.
You can find more information about the conditions for claiming mobility allowance, as well as how to apply, at the links below.
Travel and accommodation expenses
TE Office may reimburse your expenses when you need to travel to look for a job. To learn what costs can be reimbursed and on what basis, visit the TE Office's website. The decision to reimburse travel and accommodation expenses is always made by the TE Office (never by the fund).