In plain words
Those who partake of the nectar remaining from yajña attain the eternal Brahman. Even this world is not for one who performs no yajña—how then another, best of Kurus?
Word for word
Eaters of the nectar left from yajña go to the eternal brahman; this world is not for one without yajña, how [then] another, O best of the Kurus?
The commentators
Bhagavadgītābhāṣyam
एवं यथोक्तान् यज्ञान् निर्वर्त्य —
यज्ञशिष्टामृतभुजः यज्ञानां शिष्टं यज्ञशिष्टं यज्ञशिष्टं च तत् अमृतं च यज्ञशिष्टामृतं तत् भुञ्जते इति यज्ञशिष्टामृतभुजः । यथोक्तान् यज्ञान् कृत्वा तच्छिष्टेन कालेन यथाविधिचोदितम् अन्नम् अमृताख्यं भुञ्जते इति यज्ञशिष्टामृतभुजः यान्ति गच्छन्ति ब्रह्म सनातनं चिरन्तनं मुमुक्षवश्चेत् ; कालातिक्रमापेक्षया इति सामर्थ्यात् गम्यते । न अयं लोकः सर्वप्राणिसाधारणोऽपि अस्ति यथोक्तानां यज्ञानां एकोऽपि यज्ञः यस्य नास्ति सः अयज्ञः तस्य । कुतः अन्यो विशिष्टसाधनसाध्यः कुरुसत्तम ॥ ३१ ॥
In plain words
So, having carried out the sacrifices exactly as they were described —
'Enjoyers of the nectar-remnant of sacrifice' — whatever is left over from sacrifices is the sacrifice-remnant, and that remnant, being also nectar, is what is meant by 'nectar-remnant of sacrifice'; that is what they eat. So they are called 'enjoyers of the nectar-remnant of sacrifice.' Having performed the sacrifices just described, they eat, in the time left over, the food prescribed by rule and called nectar — that is why they're called this. They go on, they attain, the eternal, age-old Brahman, if they are truly seekers of liberation — this is understood to happen, of course, only eventually, with the passing of time. This ordinary world isn't even available to everyone; for someone who hasn't performed even one of the sacrifices just described, there is no world at all for him — how then could there be any other world, one reached only by special means, best of the Kurus?
Close to the Sanskrit
Thus, having completed the sacrifices as stated —
'Enjoyers of the nectar-remnant of sacrifice' — the remainder of sacrifices is 'sacrifice-remnant'; that sacrifice-remnant, and that which is nectar, is the nectar-remnant of sacrifice; that they enjoy — hence 'enjoyers of the nectar-remnant of sacrifice.' Having performed the sacrifices as described, in the time remaining from that, they eat the food prescribed by rule, called nectar — hence 'enjoyers of the nectar-remnant of sacrifice.' They go, they attain, Brahman, the eternal, the age-old, if they are seekers of liberation; this is understood by implication, with reference to the eventual passing of time. This world does not exist even as common to all beings, for one who has not even a single one of the sacrifices as described — for him there is none; how then could there be another [world], attainable only by special means, O best of the Kurus?