It is not a very controversial text - all translations of the Bible present it more or less in the same way and can be understood as a call not to leave Christian gatherings, be it a Sunday Mass or any other Sunday gathering in a different denomination. However, is it really the sense of what the Apostle Paul aims to convey in this passage? The number of meetings may vary depending on the church - from one meeting a week, usually on Sunday, to several (usually) masses a day. It is a serious issue because the ones who ‘forsake the assembling of ourselves together’ will be faced with “judgment and a burning indignation” (Heb. 10:26-29).
It is worth noting that in the text there appears a chronological reference: we have to gather until the 'day' comes. The Greek word episynagoge translated here as "assembling of ourselves together" means 'a complete collection; specifically a Christian meeting (for worship); assembling or gathering together' (Strong’s Greek Dictionary). In Heb. 10:25 it is not mentioned in the plural form, so it is not about many 'assemblings of ourselves together', but just one. What kind of assembling is it? The above mentioned episynagoge was used in the New Testament only twice. The other instance of it can be found in 2 Thes. 2:1 - "Now we beseech you, brethren, by the coming of our Lord Jesus Christ, and [by] our gathering together unto him" (KJV). So a very specific gathering is mentioned - the gathering to our Lord. Interestingly, a chronological reference appears there as well: "we beseech you, brethren, by the coming of our Lord Jesus Christ". It seems, therefore, that the 'day' mentioned in Heb. 10:25 is the time of the return (Parousia) of our Lord (see Phil. 1:6,10).
Gathering to Jesus Christ has a fundamental meaning for the called ones. He is "the head of the body, the church" (Col. 1:18 KJV) - the head of the Body of Christ, whose members are recruited from amongst the ones called in the present age (1 Cor. 12:12,13,27). The winners of this calling, "shall be priests of God and of Christ, and shall reign with him" (Rev. 20:6 KJV). However, the calling is limited in time as it shall happen until the day of Parousia, or our Lord’s second coming. Then his promise will be fulfilled for the elect ones: "I will come again, and receive you unto myself" (Jn. 14:3 KJV). After completion of the Royal Priesthood the time of blessings for the creature "subject to vanity" shall come (Rom. 8:19-22).
The above proposed understanding of "the assembling of ourselves together" that we find in Heb. 10:25 is also confirmed in the direct context. Heb. 10:19-22 - "Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus, by a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh; And [having] a high priest over the house of God; Let us draw near… (KJV). So we draw near or gather in the antitypical Sanctuary of the antitypical Tabernacle. Similarly in Heb. 12:22,23 - "But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, to the general assembly and church of the firstborn, which are written in heaven" (KJV). So it is not about this church or another, or any assembly hall, but "worship in spirit and in truth" paid by those consecrated to God's Church - the Body of Christ (Jn. 4:24). The affiliation of the ones consecrated in Christ changes from the earthly to the heavenly; we are reckoned in heaven as members of the "assembly (…) of the firstborn" and as sons of God (Rom. 8:16).
This is certainly the assembly we must not neglect. "We then, [as] workers together [with him], beseech [you] also that ye receive not the grace of God in vain. (For he saith, I have heard thee in a time accepted, and in the day of salvation have I succoured thee: behold, now [is] the accepted time; behold, now [is] the day of salvation)" (2 Cor. 6:1,2 KJV). If we have become sons of God through the faith given to us, as well as through "the token of what is to come, that is, the spirit, in our hearts" (Eph. 2:8; 2 Cor. 1:21,22 NW), then the time of salvation is right now for us. Paul urges us not to receive this grace in vain. Not only we cannot be lukewarm towards this calling (Rev. 3:15,16), but even more so, we need to "provoke unto love and to good works (...) and so much the more, as ye see the day approaching" (Heb. 10:24,25 KJV).