There are a couple ways to say something in the past tense in Greek. Scholars say that people make too much of these distinctions. But they are just that - distinctions.
The AORIST tense is a snapshot of the past. We know that something happened. We know that an event occurred. But we're not too sure about all the details of that past event and their significance. The PERFECT tense, which is rarely used in contrast to the AORIST tense, sees an event or a happening in the past as a completed action with durative and continuing effects to the present.
The first three verses of the book of Hebrews are its overture. There are many descriptive ideas in this passage. However, there are only two true verbs. The first is in 1.2. God "spoke." The second is in 1.3. The Son "sat down" [AORIST].
In Heb 1.1-3 there are six phrases that detail the person and the work of Jesus, but all of them await this verb "sat down." But why though? Who cares about Jesus sitting down? What's the deal with that? Why is it so important?
If you keep reading Hebrews you will soon see that its purpose is to show Jesus as the faithful High Priest of the New Covenant. In the OT, high priests don't sit down because their job is never finished. But not so with a perfect High Priest who offers a perfect Sacrifice.
This little verb ["sit"] is so important to the writer of Hebrews that when he gets to 8.1 he says that the main point of what he has said is this: we have a high priest who has "taken his seat" [AORIST]. The writer of Hebrews uses this verb two other times. In 10.12 he repeats the vast theological significance of the sitting [AORIST] of Jesus at the right hand of God after He suffered once and for all for sins.
It seems as though these above references to Jesus sitting are primarily to assert theological points. However, the writer of Hebrews cannot hold it in any longer. When he arrives at his last usage of the "sitting" of Jesus [12.2], an AORIST verb will not cut it.
Let us run with endurance the race that is set before us, fixing our eyes on Jesus, the Author and Perfecter of faith, who for the joy set before Him endured the cross, despising the shame, and has sat down [PERFECT] at the right hand of the throne of God.
The point of this exhortation is to show HOW and WHY the sitting of Jesus presently means something to believers who need perseverance [10.32-39, ch 11]. He is the example we should look to. He has finished His work and endured more than we ever will [2.16]. He can sympathize us [4.15]. His finished work, His sitting down... it has continually effective results right now.