Re: Suspension motion
Members frequently use the “motion to suspend the rules” to fast-track legislation that has broad support and little need for prolonged debate. When the House considers a bill under suspension of the rules, the House suspends its normal rules and procedures controlling legislative debate and votes, allowing the bill to pass quickly. The suspension process’ parameters mean that broadly bipartisan legislation is typically best suited for it.
from: https://www.progressivecaucuscenter.org/suspensions-117th-congress
Re: Suspension calendar
There is a special calendar when a suspension motion may be made.
A motion to suspend the rules may only be made by the Speaker of the
House or their designee, though it is customary for committee chairs
to write the Speaker requesting a suspension. Once a member moves to
"suspend the rules" and take some action, debate is limited to 40
minutes, no amendments can be offered to the motion or the underlying
matter, and a 2/3 majority of Members present and voting is required
to agree to the motion.
These votes, under the rules, may only take place on Mondays,
Tuesdays, and Wednesdays. Under special circumstances, suspension
votes may take place on Thursdays or Fridays, or other days...
https://en.wikipedia.org/wiki/Suspension_of_the_rules_in_the_United_States_Congress
I think the Speaker is really just saying, that he plans on bringing the new bill to the floor via a suspension motion.
Potential significance in the current situation:
If the matter under consideration was controversial, like Ukraine aid, it would be a sign that a deal was made between the party leaders, and they're using procedure to limit debate for the purpose of locking out any hold-outs still opposed to the deal.
If the matter under consideration was not particularly controversial (eg Israel aid, without the House IRS policy changes bundled to it), it wouldn't mean much.