Not necessarily expensive, just capable.
Many better quality speakers are less of an easy load for a receiver to deal with. Most receivers are fine with 6 or 8 ohm speakers, but speakers that are rated at 4ohms, or drop to 4ohms somewhere along their frequency range (usually bass), can ask too much of the receiver and they can become unstable at higher volumes because it can't give what the speaker is asking of it. If the speaker is also of a low sensitivity, this can only make things worse.
Receivers that are able to deal with these types of speakers tend to have better and more stable amplification, which does tend to come at a price. I find that the more stable receivers are around the £1k price point, which is where they start to deal with more demanding speakers, particularly 4ohm rated ones. They better able to produce transients in soundtracks, and have greater control over the speaker, allowing to 'start and stop' quicker. A receiver has to do this for five or even seven channels, and when you're adding in inefficient speakers or awkward loads, this can become too demanding for a budget receiver to cope with.
"Boxiness" is a speaker issue. If the speaker isn't well braced internally, or if the cabinet produces unwanted colorations, it is classed as boxy. This type of cabinet tends to 'give away' a speaker's position, spoiling the illusion of the three dimensional image that the drivers are trying to create. This can affect the speaker's ability to appear "transparent".
"Overblown bass" can be due to a couple of things. It can be inherent in a speaker's design to produce a lot of bass, and if the measurements show a big hump in the bass area, that's overblown. Obviously, a flat response is desired. This could also be a room issue, which can usually be minimised with the room EQ control on the AV receiver. It can also come about when an amplifier hasn't got enough control over the speaker's bass. There is a measurement for this which is called damping factor, but manufacturers only quote damping factor at a single frequency, which is pretty useless as it is a variable factor that changes with frequency. A high quoted damping factor may sound good on paper, but it doesn't tell you if the amplifier can keep low bass under control.
"Forward" is often mistook for 'bright', and bright is often mistook for 'harsh'. These three are all very different. There are plenty of amplifiers out there that sound a little soft and warm, which tends to smother detail across the entire frequency range. This can give a smooth or laid back impression. A more neutral amplifier can sound more 'forward' because there is less bass smothering and softening things, so it sounds like the while image is pushed further forward in comparison. You tend to find this with Class D amplifiers and lean sounding amplification like the Cyrus integrated amplifiers from years ago. These sort of amps do need more care when partnering with speakers so as not to come across as bright. 'Bright' is a lively treble, some may say 'extended'. This can be good for low level listening, and examples of this are the PMC DB1i speakers. It is a character that some like, some don't. And harsh is just plain unlistenable, bordering on headache inducing over a period of time. This tends to appear in the lower treble region, far below the frequencies that make something sound bright. Harsh is a very overused term as many people assume it means the same as bright.
A speaker can give the impression of better "timing" if it doesn't possess an overblown bass or a particularly extended bass. They can give the impression of sounding 'faster' than a bassy speaker. Put very simply. Very responsive speakers with extremely light drivers can also give this impression, as it can react quicker than a speaker with larger, heavier drive units.