Holiness is a very important aspect of the spiritual life, and the Popes in the 20th century certainly called on all Catholics, lay and ordained, to do whatever they could to grow in holiness.
I think holiness could be defined in many ways, but the best way is to define it as becoming as ‘Christlike’ as possible in this life. This is the summit and aim of all Christian spiritual perfection, to be united with God through Christ, and that is what the sacraments of baptism, confirmation and eucharist (to my understanding) help achieve, both by justifying and sanctifying us and by making us ‘partakers in the divine nature’ through divinising grace. Paul says in 2 Corinthians that Christians are going from ‘glory to glory’, ever better reflecting the face of the Lord in themselves as they grow in spiritual maturity and holiness, which is completed when we will not see ‘through a glass darkly’ but we will see God ‘as he is’ (1 John) ‘face to face’ (1 Corinthians 13). The perfection of the Christian life, as we can see in the great saints, is charity coming from an intimate union with God which raises the soul from its base condition of sinfulness to partaking in God’s nature through grace. This does not mean when we become holy we also become God, rather, we are conformed to God’s son in his image and move from ‘glory to glory’ as we grow in holiness.