Interpose, interfere, intervene, mediate, intercede all basically mean to come or to go between two persons, two things, or a person and thing.
Interpose (see also INTRODUCE 2 ) may be used in place of any of the succeeding words largely because it carries no further implications, except as these are derived from the context.
Interfere (see also MEDDLE ) implies a getting in the way of a person or thing whether by crossing his or its path or, more often, by creating a condition that hinders his movement, activity, or vision or its free operation or full effectiveness.
Intervene may be used with reference to something that interposes itself or is interposed between things in space or time or between persons or between a person and his interests, work, or goal.
Mediate often specifically implies intervention between those who are hostile, antagonistic, or otherwise opposed to each other, for the sake of reconciling them or settling their difficulties; mediate usually implies, as intervene need not imply, an interest in both sides or freedom from bias toward either side. But mediate may also be used abstractly in reference to something that lies between extremes or contradictories and effects either their union or a transition between them.
Intercede implies intervention on another's and usually an offender's behalf and the use of one's good offices in imploring mercy or forgiveness for him from the one who has been injured or offended.