Show on user profile page the commissions he is connected to
You’d need to query for all Matrix Blocks the user is related to using a Matrix Block ElementCriteriaModel. Unfortunatelly this is not possible from the template level by default, you need to either install the plugin Low Blocks, or write some some lines of PHP in a custom plugin.

Here’s how you would have to set the params for the Low Blocks function:

{% set userId = craft.request.lastSegment %}
{% set user = craft.users.id(userId).first() %}

{% if not user %}
    {% exit 404 %}
{% endif %}

{% set matrixField = craft.fields.getFieldByHandle('commissionmembers') %}

{% set blocks = craft.lowblocks.blocks.fieldId(matrixField.id).type('members').relatedTo({
    targetElement: userId,
    field: 'member',
}) %}

{% for block in blocks %}
    {% set commission = block.getOwner() %}

    {{ commission.title }}
    {{ block.function }}
{% endfor %}